感じ = use when you are talking about how something feels physically (ex: if you touch something and it feels rough or soft) and the impression that something gives you (ex: you look at a painting or a person and get an impression). You cannot use 感じ to talk about your physical condition (ex: if you are feeling sick or healthy) 気持ち = emotions and feelings. 言葉のニュアンスがよくわからないときは辞書の例文を読むのをおすすめします。When you don't understand the nuance of a word well, I recommend you read the example sentences in a dictionary. (It's helped me a lot!)

When modifying a noun with a verb don't use の after verb because it is ungrammatical. You can just attach the verb directly to the noun (for example: 飛んでいる感じ)